A square loop of side `a` is placed in the same plane as a long straight wire carrying a current `i`. The centre of the loop is at a distance `r` from wire where `r gt gt a`. The loop is moved away from the wire with a constant velocity `v`. The induced `e.m.f` in the loop is

Explanation

Magnetic field the straight wire of current `i` at a distance `r` is `B=(mu_(0)i)/(2pi r)`
flux associated with the loop is `phi=BA=(mu_(0)i)/(2pir) a^(2)`
`:. e=(-dphi)/(dt)=(-mu_(0))/(2pi)ia^(2)(d)/(dt)((1)/(r ))=(-mu_(0))/(2pi)ia^(2)((-1)/(r^(2)))(dr)/(dt)`
Hence the induced emf in the loop is
`e=(mu_(0))/(2pi)i(a^(2))/(r^(2))v ( because (dr)/(dt)=v)`